--- Tom <

tom@...> wrote:

> The latest info has been posted.

>

> Current information shows the difference growing

> at a rate of one additional prime every increase

> of 267 in width when looked at as a linear best fit,

> but the growth rate is tending to be concave up.

>

> A plot of k(width)-pi(width) versus width is at

> www.opertech.com/primes/trophy.jpg

> were k(width) is the number of primes in a interval.

>

> A list of first occurances (width) is at

> www.opertech.com/primes/trophycase.html

Can you briefly explain what the 'last occurance' represents. First occurance

seems obvious, assuming it's the smallest w such that a tuple of with w can be

found where k(w)-pi(w) takes the stated value, k(w) being the count of slots in

the tuple. Is the last occurance simply the w such that all larger w have a

currently known tuple with the stated delta?

That graph has a wonderful hockey-stick shape. I can think of no heuristic

which would suggest that it either ought to be asymptotically linear, or

concave up. Convex up would, however, surprise me, but again I couldn't explain

why.

Phil

Phil

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